Measuring the nuclear equation of state with neutron star-black hole mergers

Gravitational-wave (GW) observations of neutron star-black hole (NSBH) mergers are sensitive to the nuclear equation of state (EOS). We present a new methodology for EOS inference with non-parametric Gaussian process (GP) priors, enabling direct constraints on the pressure at specific densities and the length-scale of correlations on the EOS. Using realistic simulations of NSBH mergers, incorporating both GW and electromagnetic (EM) selection to ensure sample purity, we find that a GW detector network operating at O5-sensitivities will constrain the radius of a $\text{unit}[1.4]M_{\odot }$ NS and the maximum NS mass with $1.6\mathrm{\%}$ and $13\mathrm{\%}$ precision, respectively. With the same sample, the projected constraint on the length-scale of correlations in the EOS is $\ge \text{unit}[3.2]MeVf{m}^{-3}$. These results demonstrate strong potential for insights into the nuclear EOS from NSBH systems, provided they are robustly identified.